After quitting the race, Work and Pensions Secretary Stephen Crabb said Mrs May was the only candidate who could "unite our party and "form a cohesive and strong government", while eliminated former defence secretary Liam Fox stressed: "Experience matters."

After her victory, Mrs May said: "There is a big job before us: to unite our party and the country, to negotiate the best possible deal as we leave the EU, and to make Britain work for everyone.

"I am the only candidate capable of delivering these three things as prime minister, and tonight it is clear that I am also the only one capable of drawing support from the whole of the Conservative Party."

The two candidates who top the final round of MPs' votes will go forward to a postal ballot of party members to select a new Conservative leader - and prime minister - in a contest due to end on September 9.

Mrs May's dominant first-round performance and energy minister Andrea Leadsom's strong showing in second place with 66 votes paves the way for an all-woman run-off.

But Michael Gove has vowed to fight on, with his backers suggesting he will try to attract both Mr Crabb's social reformers and Dr Fox's Eurosceptics to build on the 44 MPs he won over in the first round.

But despite her overwhelming support among MPs, Mrs May will be all too aware that in the two previous contests conducted under the present rules, initial frontrunners Ken Clarke and David Davis went on to be rejected by grass roots members.

As a supporter of the Remain vote in last month's EU referendum, the Home Secretary is vulnerable to claims by Eurosceptic rivals that the largely Brexit-backing membership requires a leader who actively campaigned to Leave.

But Leave campaigner Dr Fox insisted the timing and circumstances of the contest meant Mrs May was the best placed candidate.

Speaking outside Parliament after being eliminated from the race, he said: "We have nine weeks before the candidate who is successful becomes prime minister.

"It is essential that they have an understanding at the top levels of government and of international affairs and how the process in Whitehall operates.

"And for that reason I've decided to give my support to Theresa May - I intend to work closely with her, to campaign for her, and I'm sure she will be a very fine prime minister of this country."

Mrs May has also faced criticism over her refusal to give firm assurances that EU nationals would be allowed to remain in the UK and was accused by former Cabinet colleague Ken Clarke of being a "bloody difficult woman" with little knowledge of foreign policy.

In unguarded comments caught on camera by Sky News, Mr Clarke discussed the leadership candidates with fellow Tory veteran Sir Malcolm Rifkind, saying: "Theresa is a bloody difficult woman but you and I worked with Margaret Thatcher."

He added: "I don't think either Andrea Leadsom or Boris Johnson actually are in favour of leaving the European Union."

The two Tory veterans were scathing about Mr Gove, with Sir Malcolm saying "I don't mind who wins as long as Gove comes third", while Mr Clarke warned if the hawkish Justice Secretary was in Number 10 "we'd go to war with at least three countries at once".